One of the cons of a kraton knife handle it its appearance. Kraton is a durable material, and it can be made textured to grip the hand that's holding it.
However, no amount of chemical treatment or artful design will make a kraton knife handle look like anything other than black rubber. For a working knife, this shouldn't be too much of a concern, but if you're carrying a knife for the sake of function and appearance, it helps to have something on your hip that looks good in addition to being sturdy and useful.
According to the Scrap Yard Knife Company, whose products are made from a different material called resiprene C, kraton knife handles can both absorb and emit fluids over time. This can be problematic if you use your kraton handle for skinning game or cleaning fish, or if you constantly have your knife submerged in some sorts of fluids.
Even if there's a chemical coating on your kraton handle, the fluids will get in over time, and they can damage the material, making it weaker and more brittle, not to mention odorous.
While kraton is durable and able to take vigorous use, its vulnerability to accepting chemicals and fluids can make kraton harder to keep clean than other alternatives. If you clean the handle promptly, ensuring that there's nothing left on it as soon as you've finished a task, then you can likely keep the material clean.
However, once the mess has been absorbed into the kraton, the knife handle will feel dirty until you've managed to either clean out the pores of the rubber entirely, or the kraton falls apart and needs to be replaced.